However, after a surprise recovery in the Irish property market, the value of Ulster’s loan book has increased substantially. Ross McEwan, the bank’s chief executive, has indicated his desire to stay in the Irish market, and is expected to give further indications that RBS will retain the division this week.

Ulster Bank has lost more than £2.5bn in the past two years, but managed small profits in the first two quarters of this year, and will receive a boost worth around £300m from reversing loan impairments in the three months to September, RBS said last month.

“They kept hold of it in the bad times, why wouldn’t they hang on to it in the good times?” one industry insider said.

Ulster Bank, which has about 2m customers across Northern Ireland and the Republic of Ireland, employs 6,000 people and has more than 200 branches across the two countries.

RBS took control of the company in 2000 when it bought NatWest, which had owned Ulster since 1917.

“My preference has been to hold on to that business, but we have got to find an answer for shareholders,” Mr McEwan told institutional investors on a call earlier this month.

“That market has been going well. If you look at just Dublin alone, the property prices are up 23pc over the last 12 months, which has helped us. We are seeing a path for Ireland and what we do with that business which is positive.”

The bank had considered a tie-up with Ireland’s Permanent TSB, as well as a cash injection, but has become increasingly bullish on Ulster’s prospects in recent months. The review of the operations, announced early this year, is close to completion.

RBS, 80pc owned by the taxpayer, could reveal its best quarterly operating profits since its £45bn bail-out in 2008 on Friday. The release of loan write-offs will propel it to operating profits of £1.6bn in the three months to September, although results may be hit by money set aside for fines related to foreign exchange rigging.

The bank is also expected to show a significant improvement in its capital position, owing partially to the sale of its US business, Citizens. RBS floated the bank last month and retains a 66pc share.

Analysts expect the bank to signal that its Tier 1 capital ratio, once Citizens is fully sold, will be around 13pc – up from 10.1pc in the summer.

Capital strength will be a key focus for banks this week, with the Bank of England due to reveal new rules on Friday.

The Bank will publish its review of the leverage ratio – how much a bank has to hold in reserve against its loans – while the European Banking Authority (EBA) and European Central Bank (ECB) will today release the results of their comprehensive tests of banks’ financial health.

No British banks are expected to have failed the EBA’s tests, while the ECB – which is only assessing lenders in the eurozone – is set to fail around 25.

Lloyds and Barclays are also expected to publish improvements in profits this week.